As per PC World, the Pandora streaming music service now works in NZ. I'm at work so haven't tried it on a computer, but it works on my iPhone. The app isn't yet available in NZ so I had to sign into my US iTunes account to download it. It also hasn't been updated for NZ users; it wants a 5-digit zip code but you can get around this by prefixing your NZ postcode with a 0.
Once it's set up, it seems to work well. Presumably an updated app will be available in NZ soon, making the whole process easier :)